Differencing obstruction to equidistribution
= Differencing obstruction to equidistribution
If a circle-valued sequence is not an <equidistributed sequence>, some positive-shift difference is not equidistributed either. The contrapositive follows by applying the <Van der Corput inequality for finite scalar sequences> to every nonzero integer <exponential sum>. Thus cancellation for all fixed nonzero differences implies <equidistribution> of the original sequence.